TY - JOUR
T1 - Disordered Monomer-Dimer Model on Cylinder Graphs
AU - Dey, Partha S.
AU - Krishnan, Kesav
N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
PY - 2023/8
Y1 - 2023/8
N2 - We consider the disordered monomer-dimer model on cylinder graphs Gn , i.e., graphs given by the Cartesian product of the line graph on n vertices, and a deterministic finite graph. The edges carry i.i.d. random weights, and the vertices also have i.i.d. random weights, not necessarily from the same distribution. Given the random weights, we define a Gibbs measure on the space of monomer-dimer configurations on Gn . We show that the associated free energy converges to a limit and, with suitable scaling and centering, satisfies a Gaussian central limit theorem. We also show that the number of monomers in a typical configuration satisfies a law of large numbers and a Gaussian central limit theorem with appropriate centering and scaling. Finally, for an appropriate height function associated with a matching, we show convergence to a limiting function and prove the Brownian motion limit around the limiting height function in the sense of finite-dimensional distributional convergence.
AB - We consider the disordered monomer-dimer model on cylinder graphs Gn , i.e., graphs given by the Cartesian product of the line graph on n vertices, and a deterministic finite graph. The edges carry i.i.d. random weights, and the vertices also have i.i.d. random weights, not necessarily from the same distribution. Given the random weights, we define a Gibbs measure on the space of monomer-dimer configurations on Gn . We show that the associated free energy converges to a limit and, with suitable scaling and centering, satisfies a Gaussian central limit theorem. We also show that the number of monomers in a typical configuration satisfies a law of large numbers and a Gaussian central limit theorem with appropriate centering and scaling. Finally, for an appropriate height function associated with a matching, we show convergence to a limiting function and prove the Brownian motion limit around the limiting height function in the sense of finite-dimensional distributional convergence.
KW - Central limit theorems
KW - Disordered systems
KW - Monomer-dimer models
KW - Random dimer activities
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U2 - 10.1007/s10955-023-03159-7
DO - 10.1007/s10955-023-03159-7
M3 - Article
AN - SCOPUS:85168455180
SN - 0022-4715
VL - 190
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
IS - 8
M1 - 146
ER -